Find the Exact Value tan(60)

Problem

tan(60^∘)

Solution

1. Identify the angle on the unit circle. The angle 60^∘ corresponds to the coordinates (x,y)=(1/2,√(,3)/2)

2. Apply the formula for the tangent function in terms of sine and cosine.

tan(θ)=sin(θ)/cos(θ)

3. Substitute the known values for sin(60^∘) and cos(60^∘)

tan(60^∘)=√(,3)/2/1/2

4. Simplify the fraction by multiplying by the reciprocal of the denominator.

tan(60^∘)=√(,3)/2⋅2/1

tan(60^∘)=√(,3)

Final Answer

tan(60^∘)=√(,3)

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